The triple integral fff f(x, y, z)dV, given that D= [-2, 2] × [0, 6] x [1, 4] is equal to: Select one: O A. ff ²₂ f(x, y, z)dxdydz OB. f f f f(x, y, z)dydzdx OC. ff 2₂ f(x, y, z)dzdxdy O D. None of the choices OE ²₂ f f(x, y, z)dxdydz

Q: Find div F for F(x. y, 2) = (xy, 5 - zy, x +y). Select the correct answer below: O x- O y-? O x-5- O…

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Q: Let z = x +3xy+ 2y . Find and

A: Given function is z= x^2 +3xy +2y^2

Q: Find 4rye®y? dA, where R [0, 1] × [0, 2]. R

A: The objective is to find the double integration where  R=[0,1]×[0,2]

Q: 2. For F = (xz3, 2y*x²,5z?y) find: a. div F b. Curl F and find div(curl F) C.

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Q: Evaluate f C F = (x² +

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Q: Find d = gcd (270, 105) and hence find integers x , y such that d = 270x +105y .

A: GCD stands for greatest common divisor for two or more numbers.

Q: -dx. (3x² + 1)ª Evaluate -1 +C OA. 18(3x² + 1)³ O B, In(3x2 + 1)ª) +C 1 OC. + C 18(3x² + 1)³ x2 +C…

A: Given- ∫x3x2+14 To find- The value of the integral

Q: Find V. (F × G), if F(x, y, z) = 5xi +j+ 7yk and G(x, y, z) = xi+yj – zk. - V. (F × G) =

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Q: 2x Eyaluate dx . 1-4x4

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Q: Calculate (2x+3y+z)dV where = [1,2] x [-1,1] × [0,1] A. 0 B. 1 C. 4 D. 7

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Q: Find f f(x,y) dA, where f(x, y) = x and R = [5, 10] × [-5, –4]. SSR f(x, y) dA=

A: The given function is f(x,y)=x, and the domain is x,y∈5,10×-5,-4. To Evaluate: ∬Rf(x,y)dA.

Q: Find V · (V x F), if F(x, y, z) = 5e*?i+ 9xe"j – 6e²k. V · (V × F) =

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Q: Evaluate dxdy √√3x + 4y over the rectangle [0,3] × [0,4].

A: We find required integral by using Fubinis method.

Q: Solve the given differential equation. 3xvdv + (2v² – 1)dæ = 0 O (2u – 1)° = Cx* O (2u² – 1)°xª = C…

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Q: Evaluate [², dx V4-x2 2.

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Q: Find f,, fy, and f, for f(x,y,z)= 5xy+ 3xz + yz.

A: It is partial derivative

Q: ind V. (V × F), if F(x, y, z) = = V. (V X F) = ezi+ 6xe¹j - 3ek.

A: Topic:- vector algebra

Q: Find f if Vf = 10xyi+ (5æ² + 5y^) j f =

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